Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Watersheds in Digital Spaces: An Efficient Algorithm Based on Immersion Simulations
IEEE Transactions on Pattern Analysis and Machine Intelligence
Watershed of a continuous function
Signal Processing - Special issue on mathematical morphology and its applications to signal processing
Topographic distance and watershed lines
Signal Processing - Special issue on mathematical morphology and its applications to signal processing
A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model
International Journal of Computer Vision
Diffusion Snakes: Introducing Statistical Shape Knowledge into the Mumford-Shah Functional
International Journal of Computer Vision
Watersnakes: Energy-Driven Watershed Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Energy Partitions and Image Segmentation
Journal of Mathematical Imaging and Vision
Spatially adaptive wavelet thresholding with context modeling for image denoising
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
A binary level set model and some applications to Mumford-Shah image segmentation
IEEE Transactions on Image Processing
Level Set Segmentation of Cellular Images Based on Topological Dependence
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing
Four-Color Theorem and Level Set Methods for Watershed Segmentation
International Journal of Computer Vision
Robust Segmentation by Cutting across a Stack of Gamma Transformed Images
EMMCVPR '09 Proceedings of the 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Segmentation of Neural Stem/Progenitor Cells Nuclei within 3-D Neurospheres
ISVC '09 Proceedings of the 5th International Symposium on Advances in Visual Computing: Part I
Segmentation of complex nucleus configurations in biological images
Pattern Recognition Letters
Segmentation of neuronal nuclei based on clump splitting and a two-step binarization of images
Expert Systems with Applications: An International Journal
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In this work a marker-controlled and regularized watershed segmentation is proposed. Only a few previous studies address the task of regularizing the obtained watershed lines from the traditional marker-controlled watershed segmentation. In the present formulation, the topographical distance function is applied in a level set formulation to perform the segmentation, and the regularization is easily accomplished by regularizing the level set functions. Based on the well-known Four-Color theorem, a mathematical model is developed for the proposed ideas. With this model, it is possible to segment any 2D image with arbitrary number of phases with as few as one or two level set functions. The algorithm has been tested on real 2D fluorescence microscopy images displaying rat cancer cells, and the algorithm has also been compared to a standard watershed segmentation as it is implemented in MATLAB. For a fixed set of markers and a fixed set of challenging images, the comparison of these two methods shows that the present level set formulation performs better than a standard watershed segmentation.